This project is designed to use mathematical and computational methods to develop models of the morphology of individual dendrites, whole neurons, and neuron networks that are based on experimental data. Several projects have continued during FY2001. The first continues a theoretical analysis of why neuronal dendrites branch, based on morphological data obtained earlier in this laboratory. Using the symbolic manipulation package Mathematica, we have continued to investigate why the dendrites of most neurons branch extensively. The simplest hypothesis - that branching maximizes surface-to-volume ratios - can be falsified with a trivial counter-example. Our current view is that neurons that must receive large numbers and/or a great variety of synaptic contacts have to branch extensively in order to optimize packing density within the neuropil. The key element seems to be the volume fraction occupied by afferent axons, which can vary over a wide range depending on the organization of pre- and postsynaptic elements that must be accommodated. This hypothesis is completely consonant with our earlier hypothesis that dendrites branch in order to maximize the amount of synaptic current that can be delivered to the soma from synaptic sources that are distributed at relatively low density throughout the neuropil. Optimized models produce dendrites that resemble those in the target set of 60 dendrites from reconstructed cat motoneurons. We conclude that the ratio of external coupled volume to internal dendrite volume is a realistic figure of merit for neurons, and that motoneuron dendrites come reasonably close to optimal shapes for this figure of merit. This work has continued with development of a model approach that can successfully reproduce the complex three-dimensional morphology of cat spinal motoneurons in order to infer the importance of intrinsic versus extrinsic influences on the anatomy of nerve cells. We have also continued to improve work on visualizing the neuronal interactions that occur within the basic circuit that produces rhythmic respiration, based on experiments of Dr. Jeffrey Smith. The simulations permit visualization of the synchronization of individual neurons within the circuit, as well as the sequence of synaptic flows and membrane dynamics among the five cell types that shape the time course of respiration. We have begun a new project that concerns a computer modeling study of the effects of beta innervation of muscle spindles in mammals. Muscle spindles contain specialized muscle fibers that are innervated by two types (static and dynamic) of gamma motoneurons that do not receive direct feedback from group Ia muscle spindle afferents. However, it is clear that many spindles also receive beta innervation from the motoneurons that also innervate the extrafusal skeletal muscle fibers that form the main bulk of muscles and that do receive powerful group Ia excitation. The effects on muscle spindle afferents differ depending on whether the beta motoneurons innervate fast or slow twitch extrafusal muscle fibers. The functional consequences of this positive feedback remain unclear. Because the system is so complex, we are developing a multiple neuron simulation system that will enable us to explore the probable influence of positive excitatory feedback due to beta innervation among alpha and beta motoneurons. Finally, we are accumulating data on the morphology of motoneurons in the neonatal mouse spinal cord, labeled intracellularly with Biocytin. The cells are completely reconstructed and the data will be analyzed quantitatively using methods developed in collaboration between this laboratory and scientists at the Krasnow Institute of George Mason University. The data will form part of an extensive data base being developed as part of the Human Brain Project that is designed to permit scientists anywhere to access and analyze morphological data on many types of neurons.